If a custom operation is defined as x × y = x + y + x*y, what is the value of 6 × 24?

Introduction / Context:
This problem introduces a custom binary operation on numbers. Such questions frequently appear in aptitude and reasoning sections to test whether the candidate reads definitions carefully instead of assuming the usual meaning of mathematical symbols like multiplication. You must apply the given definition exactly as stated.

Given Data / Assumptions:

• The operation × is not ordinary multiplication.
• It is defined by the rule: x × y = x + y + x*y.
• We need to compute 6 × 24 using this special rule.

Concept / Approach:
Whenever a new operation is defined, always replace the symbol with the given formula. Here, for any numbers x and y, we must calculate x + y + x*y. That means we first find the product x*y, then add x and y to this product. We never treat × as normal multiplication in this context, even though the same symbol is used.

Step-by-Step Solution:
Step 1: Identify x and y in the expression 6 × 24. Here x = 6 and y = 24. Step 2: Use the definition x × y = x + y + x*y. Step 3: Compute the product x*y = 6*24 = 144. Step 4: Compute x + y = 6 + 24 = 30. Step 5: Add these results: 144 + 30 = 174. Step 6: Therefore, 6 × 24 under the given operation equals 174.

Verification / Alternative check:
We can quickly check by recomputing: 6*24 = 144 and 6 + 24 = 30. Adding them again gives 174, confirming that our arithmetic is consistent. There is no other interpretation for the custom operation given, so 174 is the unique correct value for this question.

Why Other Options Are Wrong:
Option 150 might come from adding 6 and 24 to the normal product 120 instead of 144. Option 186 could come from a mistaken product like 6*27 instead of 6*24. Option 210 may be the usual product 6*35 or a random guess that ignores the definition. Option 144 corresponds only to the ordinary product 6*24 and does not include x + y, so it does not satisfy the rule x × y = x + y + x*y.

Common Pitfalls:
A very frequent mistake in such questions is to interpret the symbol × as normal multiplication without using the new definition at all. Another pitfall is to partly apply the rule, for example adding only one of the numbers to the product instead of both x and y. Always rewrite the custom operation explicitly in terms of standard operations to avoid confusion.

Final Answer:
Therefore, using the custom rule x × y = x + y + x*y, the value of 6 × 24 is 174.